Editorial
MathFinance Conference Recap
The 19thMathFinance Conference we held in Frankfurt on 8-9 April 2019 was once more the key event in Germany for quants. More than 110 registered participants attended.
In a market with more standardization and regulation, and a never –ending Brexit drama, quantitative modeling is vitally important. We included a symposium on crypto currency markets with several top research result of Humboldt University.
Some of the key abbreviations and words resounding throughout the Conference were:
Social alpha, WUCA, GRIX, volunga, revga, Threshold Bipower Variation, pailab, fractional Brownian motion, ARIMA t-EGARCH, martingale defect, bufga, tensor flow, DNN, WoodF, Hurst coefficient.
Let me recap what I learned:
The first morning Natalie Packham organized a symposium on Crypto Currencies selecting key innovations from Humboldt University.
- Wolfgang Härdle explains how Pricing Crypto Currency Options works in the Case of CRIX and Bitcoin.CRIX is crypto currency index. Crypto trading has succeeded as it avoids the middle man, i.e. the traditional bank fees for EUR/USD spot trades can be circumvented. Half the world is ‘unbanked’, but smartphoned. He proposes pricing options with a SVCJ model, i.e. stochastic volatility with correlated jumps. It is not at all surprising that crypto currencies bring the jumps back to the quants’ attention, in particular with a Duffie, Singleton and Pan (2000) revival. Jumps in spot and variance occur with correlation ρj. Data to calibrate the model is available for free on coin gecko. For prop traders Härdle noted that the bitcoin price typically seems to rise when he is speaking on a crypto conference.
- Alla Petukhina derives in her talk about Portfolio Optimization with CoVar in Cryptocurrency Marketsempirical results showing a high potential of crypto-currencies for portfolio hedging and improving the risk-return profile of portfolios.
- Niels Wesselhöft Separates the Asset Universe from Crypto Currencies. In his phenotypic analysis he seeks to find out what defines crypto currencies. Statistical analysis of CRIX data vs. classic indices exhibits extremely heavy tails and can be considered the number one driving factor. This distinguishes crypto currencies from fiat currencies and stocks. The memory factor is strongest for commodities. Thus crypto currencies also differ from commodities.
- Junkie Hu presents an Empirical Studyon Realized Crypt Currency Volatility Forecasting with Jumps. One of his main questions is whether crypto volatility is unpredictable? Why is the realized volatility so high in a market that trades 24/7? Using a Threshold BiPower Variation (TBPV), he shows that investors gain higher economic value by modeling jumps, and furthermore longer investment horizons yield higher utility.
Some highlights of our panel discussion, moderated by Frank Thole (Partner at Wepex) Adrian Marcu (FX Options trader at Resilience) states that crypto is the payment method of the future, after some consolidation. It all depends crucially on block chain technology, a big added value to the world. Fiat money is also only a trust-based system. He sees the future in bank-free transaction banking. In fact, regulation in Switzerland has woken up. This means that a security token is better than the security itself. Thus, crypto is not just crypto currency. He confirms that we will need banking, but not necessarily banks, which is a huge opportunity for crypto currencies. Roger Wurzel, as former equity derivatives trader, points out that settlement, which traditionally can take you days, now requires just milliseconds. However, it took Eurex 20 years to develop its current technology. Biggest system difference is regulation. Burak Özgelen, co-founder of the Global Crypto Currency Exchange (Gloccex) explains that there is no bridge between traditional and crypto markets. Currently crypto currencies are separated from traditional trading. Consequently, we need exchanges, need regulation, so banks are allowed to invest. The goal should be to create new eco system, get new fair pricing, and combine all assets in a platform to access all other systems, including derivatives. Wolfgang Härdle supports the relevance of banking as opposed to banks providing transactions as a service. In his view, the prosumer concept includes all smart contracts, as for example in real estate, where brokers will be cut out. This is possible with this completely new data class, that allows 24/7 trading. Adrian further points out that crypto currency exchanges should include custody and security; after a run-up, there is clear need to invest: market participants need a security to invest. Most investors look for funds; investment products have to be tradable, bankable, clearable. We are back at the requirement of linking crypto currencies with the traditional markets. Wurzel poses the question how a trader would hedge its position. There must be a process how you trade with an unregulated entity. He explains that there must a custodian. It must be clear where you keep your assets. The question may not come up for 1 USD, but how about 100M USD? Investment firms demand a traditional environment.
Will crypto currencies stay? What are the practical challenges? Marcu identifies as key practical challenge that one would ideally have decentralized exchanges, but we are currently far away from that, and hence probably need a centralized exchanges first. While governments are afraid that thieves are moving value with crypto currencies, it is clear that this happens with fiat money too. In his view, exchanges are not a main game changer, but are to stay. Özgelen adds that the consumers need education. For humanity to tell the source of digital money, we need to solve the liquidity challenge, we need more exchanges, and more education. Härdle is convinced that we humans will get used to it. Wurzel supports the CRIX index having been created, as it helps the educational process. He compares equity trading in Dubai with crypto trading in Europe: There are high transaction costs, complicated procedures to open an account, high fees. Marcu makes everybody aware that if people are forced to keep only traceable, electronic money, they are forced to take the counterparty risk of a commercial bank. Erik Vynckier from the audience adds that there is a value in using traditional T+2 as a settlement as it enables entities to prove what they have done. Marcu furthermore comments that exchanges tended to show higher trading volume than actual, to attract more volume. Generally, one should be careful not to over interpret market data. Erik Vynckier also advises to distinguish price quotes from prices of actual transactions.
The conference proceeded with more highlights:
Thorsten Schmidt defined Statistical Arbitrage as a “hopefully profitable strategy”. Basically, one can think of a carry trade. You repeat it often enough with a stop-loss strategy and it will hopefully work out profitable. A binomial tree example explains the approach very clearly. In the next edition, he will include transaction costs.
Martin Simon tries to predict Stock Price Bubbleswith a forward looking indicator. The approach is motivated by using a strict local martingale. This textbook example we once learned at university can actually be useful: Using a zero strike call with vol(S)=S^2 as an example he shows that the martingale defect is what’s required in addition to the risk-neutral call option value. Invoking the new theorem by Jacquier/Keller-Ressel (2018) we obtain an explicit formula for the martingale defect in the log-normal SABR model. Overall, the option-based forward looking indicator can point to mismatches between the market value and intrinsic value of a stock.
Daniel Oeltz explains Pailab – Audit, Revisioning and Analysis of Machine Learning in Finance: Taking the view of a software developer, he addresses the question how to make the development audit safe, i.e. how to version and track changes of different models. How to analyze changes between different versions and finally how to deploy these algorithms into a production setting?Remembering that we work in a regulated market, we need to make black-box models explicable.
Markus Becker takes us through Arbitrage and Non-linear Taxes. With tax liabilities that are a convex function of the tax base, he identifies a new kind of arbitrage: trading strategies where the gains from trades remain unchanged if this strategy is applied multiple times. He calls these strategies ‘bounded’ arbitrage opportunities. He provides a complete characterization based on properties of the tax liability function as to whether bounded as well as unbounded arbitrage opportunities will exist.
Christian Kappen examines Derivative pricing: A pattern-matching problem? He presents a detailed case study how to price Bermudan swaptions using a deep neural network. This can help real-time pricing and risk management of path-dependent derivatives. He main finding is that deep neural networks (DNN) provide accurate approximations of pricers consuming high-dimensional input data.
Adil Reghai continued the LSV saga by Real Time management with local stochastic volatility. Motivated by traders, it is known that a local volatility implied dynamic is not consistent with the market observed dynamic. He quantifies the cost of the vanna-hedge (and promised to deliver the volga-part next year). By face-lifting the payoff, his approach permit a local volatility pricing and hedging in real-time, taking into account the complex dynamic of the volatility surface. We learned it is helpful to use the “wrong payoff with the wrong model to get the right pricing and hedging process.”
Maximilian Mair Estimates Volatility Surfaces via Functional Approximation and Machine Learning. His main motivation is to have a plan B estimation of the implied volatility when market is illiquid or closed, i.e. generate an intelligent guess to propose to market making trader. Empirical projection reduces out-of-sample error further when compared to traditional PCA.
Karel in’t Hout can apparently handle any dimension in his Numerical Valuation of Bermudan Basket Options via Partial Differential Equations, which has all been derived viahuman learning. He implements the PCA-based approximation brought up by Reisinger and Wittum in 2007. The numerical implementation can be reduced to one 1-dimensional PDE and 99 2-dimensional PDEs (which can be solved by ADI, you bet) and even better: the numerical solution can be performed in parallel.
Matthieu Mariapragassam presents Efficient Pricing of FX Volatility Swaps in LSV Models. Volatility swaps (more than variance swaps) have become a flow product for asset managers and leveraged funds. Therefore the many pricing requests for 1Month in G10 currencies and MXN, TRY, KRW and SGD must be handled with high speed and precision. Using Wood F distribution he effectively calculates the vol of vol correction factor. Along with a PDE approach this is the current method of choice.
Antoine Jacquier updated his talk title to New advances on Rough Volatility: Pricing and Hedging. Modeling volatility with a geometric fractional Brownian motion (instead of a jump diffusion), it is called rough if the Hurst coefficient H is less than one half. In fact, H≈ 0.1 for both equity and G10 FX. His main conclusions are
- Rough volatility models reproduce both the observed dynamics of volatility and the short-term implied volatility skew;
- Working with forward variance allows to recover martingale techniques, develop efficient Monte Carlo and asymptotic pricing and hedging methods;
- Log-normal rough volatility models remain inconsistent with VIX option smiles;
- A volatility modulated Volterra process allows generating VIX smiles consistent with the market while preserving some simplicity of log-normal modeling.
Ingo Mainert’s key note on Current Challenges and Developments of the Investment Industry made us realize finally that the world has changed. In fact, the overall returns in 2018 across markets were worse than in 2008, the year of the financial crisis, just more silent. The winning formula for asset managers in the next 10 years will be the combination of
- Sustained alpha generators, distinguished by a unique edge in investing and consistent performance;
- Broad based scale manufacturers, distinguished by low cost and unconstrained capacity;
- Solution providers, distinguished by advisory customized to clients’ needs.
Griselda Deelstra solves the problem of the smile of illiquid cross in her talk on Multivariate FX Models with Jumps: Triangles, Quantos and Implied Correlationusing Lévy processes both the reciprocal (USD-EUR instead of EUR-USD) and the ratio of two spot rates remain in the same model class. The special choice of a Variance Gamma process allows a good preservation of tail dependence. She shows case studies for Quanto Nikkei futures and the EUR-CHF-USD currency triangle.
Rolf Poulsen concludes with his collection on The Fed isn’t Federal and other Odd Things in Finance. Hedge funds don’t hedge, the French data is mostly from the US, and default isn’t default, more of which can be found in his column in Wilmott.
Overall, I learned a lot from all the speakers. I would like to thank all the speakers and sponsors to help make this conference the key content-driven event for quants. Many aspects of crypto currencies have been discussed and it appears that they will stay. While the internet has provided the tool to exchange information, block chains provide to tool to exchange anything of value. It turns out that mathematical finance is a core asset of the financial industry. Common concepts of jump diffusion models, face-lifting and fractional Brownian model are recycled. Even strictly local martingales are back, now for the asset managers to detect stock price bubbles. When I look at the stunning results of our speakers, machine learning appears to be still less productive than human learning. The show must go on.
Watch the conference video
We hope to see you all again at our future events.
Save the next conference date: 30-31 March 2020.
Uwe Wystup
Managing Director of MathFinance
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